3+q(8+-4q)+-8q=0

Solution for 3+q(8+-4q)+-8q=0 equation:

Simplifying
3 + q(8 + -4q) + -8q = 0
3 + (8 * q + -4q * q) + -8q = 0
3 + (8q + -4q2) + -8q = 0

Reorder the terms:
3 + 8q + -8q + -4q2 = 0

Combine like terms: 8q + -8q = 0
3 + 0 + -4q2 = 0
3 + -4q2 = 0

Solving
3 + -4q2 = 0

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4q2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4q2 = 0 + -3
-4q2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4q2 = -3

Divide each side by '-4'.
q2 = 0.75

Simplifying
q2 = 0.75

Take the square root of each side:
q = {-0.866025404, 0.866025404}